In the beginning after you defeat the lead hydra all the other heads are supposed to explode. But if you go back through the level you can see two guys fighting a hydra head.
In the beginning level cutscene when Kratos opens the captain's door, his skin color is normal and not the pale white it is supposed to be.
In the level "The Gate Keeper", the giant bull you fight against brakes the door door. Even so, after you defeat him the door is closed again.
The Oracle of Athens is wearing 21st century style underwear under her dress. This may be because the underwear of the time period was too revealing, and the creators wanted to keep an M rating.